QJs vs 86s: preflop equity

Before any board card is dealt, QJs holds 63.88% equity against 86s, which leaves 86s with 36.12%.

QJs

63.88%

Wins 63.44%, ties 0.89%

86s

36.12%

Wins 35.67%, ties 0.89%

Equity counts a tie as half a win. Exact over every board.

QJs against 86s: the numbers

Exact preflop results for QJs against 86s, in percent
HandWinsTiesLosesEquity
QJs63.4390.88835.67363.883
86s35.6730.88863.43936.117

Each side holds one of the suited hands: QJs and 86s. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.

That is a modest edge, the kind that shows up over many hands and is easy to miss in one. About 0.89% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.

Ranked by equity against a random hand, QJs is number 28 of the 169 starting hands and 86s is number 110.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QJs17,380,000243,0009,773,000
86s9,773,000243,00017,380,000

Exact total: 16 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.

QJs against 86s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QJs1.7691.5762.8030.565
86s0.5652.8031.5761.769

The final column gives the least the pot must offer for each unit called for a call to break even at this equity.

Who is ahead on which flops

QJs prefers rainbow flops topped by a ten or better, where it holds 71.18%, and likes low rainbow flops (nine high or lower) least, where it holds 38.30%. 86s is ahead on low rainbow flops (nine high or lower), even though it trails QJs when every flop is counted.

QJs against 86s by flop texture, in percent
FlopShare of flopsQJs winsTies86s winsQJs equity
Rainbow, ten or higher24.59570.9790.40228.61971.180
Rainbow, nine or lower6.31437.9980.61361.38938.304
Two-tone46.72763.1910.41336.39663.397
Monotone5.27359.2453.51937.23661.005
Paired17.09163.9602.17433.86665.047

A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.

Compared with a random hand

Compared with a random opponent, this matchup shifts QJs from 60.26% by +3.62 points and 86s from 46.24% by -10.12 points.

QJs and 86s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QJs, all flops63.88360.259+3.6241.06014
QJs, rainbow, ten or higher71.18060.259+10.9211.18123
QJs, rainbow, nine or lower38.30460.259-21.9550.63566
QJs, two-tone63.39760.259+3.1381.05208
QJs, monotone61.00560.259+0.7461.01238
QJs, paired65.04760.259+4.7881.07946
86s, all flops36.11746.243-10.1260.78103
86s, rainbow, ten or higher28.82046.243-17.4230.62323
86s, rainbow, nine or lower61.69646.243+15.4531.33417
86s, two-tone36.60346.243-9.6400.79154
86s, monotone38.99546.243-7.2480.84326
86s, paired34.95346.243-11.2900.75585

Does a shared suit matter?

When the hands share a suit, QJs holds 66.29%; when they do not, it holds 63.08%. QJs does better with a shared suit, by 3.21 points.

QJs against 86s by suit overlap, in percent
DealsSpecific dealsShare of dealsQJs winsTies86s winsQJs equity
Share a suit425.0065.7950.98533.22066.288
No shared suit1275.0062.6540.85536.49163.081

How often this matchup comes up

How often does it happen? 16 of the 1,624,350 ordered deals (0.0010%) are QJs against 86s, and 32 (0.0020%) if either hand may sit in either seat.

A worked example

Take a $200 pot built from $100 each. QJs' equity of 63.88% is worth $127.76, a $27.76 edge, and 86s' 36.12% is worth $72.24, which is $27.76 under its stake.

Think in thousands: about 634 of 1,000 go to QJs, about 357 go to 86s, and about 9 are chopped.

The same matchup from the other side

One page covers both views. From 86s' side the equity is 36.12%, and from QJs' side it is 63.88%.

The calculator link fills in QsJs against 8h6h, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.

How this was computed

The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 16 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.

Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.

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